I've tried and tried to think of that, maybe...
of course the deviled eggs could easily be served as an appetizer.
You could make tiny tomato sandwiches as an appetizer.
It really wasn't until the late 70s that we really had 'appetizers' much and it was the stuff we all think of as the classic retro stuff - pigs in blankets, spinach dip, shrimp dip, etc.
What about serving 'Southern style' chicken wings - fry them like you would southern fried chicken rather than serving full pieces of fried chicken. Serve with small bit sized biscuits.
You could serve small bite sized biscuits with all sorts of jams and jellies - strawberry, blackberry, peach preserves, fig preserves were BIG, pear preserves, plum jelly or order some muscadine, pawpaw or mayhaw jams & jellies - those are REAL Southern! (Bainbridge & Sussies are two good brands) We used to go into the woods to gather the muscadines and scuppernong and little pink plums not the plums we see in grocery stores - they had a completely different flavor.
We also would by those little 'cake' shortcakes in the grocery store and layer them with fresh strawberries that had been sliced and sweetened and either the whipped cream out of a can or Cool Whip.
We made sweet tea (REALLY SWEET) and then would muddle some mint leaves in it.
About the only soup we had was my grandmother's vegetable soup that she canned and then we would sometimes add some ground beef or shredded chicken.
We did stuffed bell peppers just with rice and ground beef and tomato sauce - you might could use a smaller pepper that is not a true bell pepper but similar to make these into an appetizer or get some bell peppers that have say 3 to 4 really well cupped sections and carefully cut it apart to make into 'boats'.
OH - we did put just fresh banana peppers on the table and later we started serving wedges of them with ranch dip.
It's not real old fashioned Southern cooking but you could make a black eye pea salsa and serve that.
Peanuts - we did boiled peanuts and that would work as an appetizer, we also parched them, fried them and topped off with seasonings.
Pecans - we seasoned them with worchestershire, butter, salt, garlic salt and such and then baked them.
It's not at all uncommon to see small 2 or 3 bite sized pecan or chess pies - not an appetizer but a good finger food. And of course tassies were always popular at the ladies luncheons.
I think one other thing we used to see that I don't see that might work would be Benedictine finger sandwiches. And sometimes just plain old cucumber sandwiches.
I'm rambling but I am just trying to think of what you could do.
OH - pickled okra and homemade sweet pickle chips - thick and crunchy - candy like not your normal pickles (I make a shortcut version by taking whole dill pickles and slicing them thick. Layer in a jar with sugar and pickling spice and let them sit a week or two - they candy and make their own syrup.)
Caramel cake, coconut cake, etc. for desserts